# Modified second-order generalized integrators with modified frequency locked loop for fast harmonics estimation of distorted single-phase signals (LONG VERSION)

## TL;DR

This paper introduces modified second-order generalized integrators (mSOGIs) combined with a modified frequency locked loop (mFLL) for rapid and accurate harmonic estimation in distorted single-phase power signals, outperforming standard methods.

## Contribution

The paper presents a novel combination of mSOGIs and mFLL for fast harmonic estimation with prescribed settling time, applicable to both constant and time-varying fundamental frequencies.

## Key findings

- mSOGIs achieve faster harmonic estimation than standard SOGIs.
- The combined mSOGI and mFLL approach improves accuracy in frequency tracking.
- Validation shows superior performance over adaptive notch filters.

## Abstract

This paper proposes modified Second-Order Generalized Integrators (mSOGIs) for a fast estimation of all harmonic components of arbitrarily distorted single-phase signals such as voltages or currents in power systems. The estimation is based on the internal model principle leading to an overall observer system consisting of parallelized mSOGIs. The observer is tuned by pole placement. For a constant fundamental frequency, the observer is capable of estimating all harmonic components with prescribed settling time by choosing the observer poles appropriately. For time-varying fundamental frequencies, the harmonic estimation is combined with a modified Frequency Locked Loop (mFLL) with gain normalization, sign-correct anti-windup and rate limitation. The estimation performances of the proposed parallelized mSOGIs with and without mFLL are illustrated and validated by measurement results. The results are compared to standard approaches such as parallelized standard SOGIs (sSOGIs) and adaptive notch filters (ANFs).